It will touch the x-axis and not cross it.
It will touch the x-axis once.
It would not touch or intersect the x-axis at all.
A quadratic function will cross the x-axis twice, once, or zero times. How often, depends on the discriminant. If you write the equation in the form y = ax2 + bx + c, the so-called discriminant is the expression b2 - 4ac (it appears as part of the solution, when you solve the quadratic equation for "x" - the part under the radical sign). If the discriminant is positive, the x-axis is crossed twice; if it is zero, the x-axis is crossed once, and if the discriminant is negative, the x-axis is not crossed at all.
The zeros of a quadratic function, if they exist, are the values of the variable at which the graph crosses the horizontal axis.
Yes.
If the discriminant is negative, the equation has no real solution - in the graph, the parabola won't cross the x-axis.
Once.
It will cross the x-axis twice.
It will touch the x-axis once.
It would not touch or intersect the x-axis at all.
-1 -18 -25 -7
The graph will cross the y-axis once but will not cross or touch the x-axis.
No, it will be entirely above the x-axis if the coefficient of x2 > 0, or entirely below if the coeff is <0.
It will touch it at exactly 1 point. If a quadratic function is given as f(x) = ax2 + bx + c, let the discriminant be denoted as D. Then the graph of y = f(x) will cross the x-axis at the x-values x = (-b + sqrt(D))/(2a) and x = (-b - sqrt(D))/(2a). When the discriminant D = 0, these 2 x-values are actually the same. Thus the graph will touch the x-axis only once.
If the discriminant = 0 then the graph touches the x axis at one point If the discriminant > 0 then the graph touches the x axis at two ponits If the discriminant < 0 then the graph does not meet the x axis
A quadratic function will cross the x-axis twice, once, or zero times. How often, depends on the discriminant. If you write the equation in the form y = ax2 + bx + c, the so-called discriminant is the expression b2 - 4ac (it appears as part of the solution, when you solve the quadratic equation for "x" - the part under the radical sign). If the discriminant is positive, the x-axis is crossed twice; if it is zero, the x-axis is crossed once, and if the discriminant is negative, the x-axis is not crossed at all.
-7,-25